Time-reversible implementation of MASH for efficient nonadiabatic molecular dynamics

TL;DR

This paper introduces time-reversible, higher-order integrators for the MASH method, enabling more efficient and accurate nonadiabatic molecular dynamics simulations by allowing larger time-steps.

Contribution

The authors develop and demonstrate time-reversible, piecewise-continuous integrators for MASH, improving efficiency and accuracy over standard implementations.

Findings

Global error is $ ext{O}( ext{Δ}t^2)$ with the new methods.

Larger time-steps can be used for the same error tolerance.

MASH can be implemented more efficiently than other surface-hopping approaches.

Abstract

In this work, we describe various improved implementations of the mapping approach to surface hopping (MASH) for simulating nonadiabatic dynamics. These include time-reversible and piecewise-continuous integrators, which is only formally possible because of the deterministic nature of the underlying MASH equations of motion. The new algorithms allow for the use of either wave-function overlaps or nonadiabatic coupling vectors to propagate the spin, which encodes the electronic state. For a given time-step, $\Delta t$, it is demonstrated that the global error for these methods is $\mathcal{O}(\Delta t^2)$ compared to the $\mathcal{O}(\Delta t)$ error of standard implementations. This allows larger time-steps to be used for a desired error tolerance, or conversely, more accurate observables given a fixed value of $\Delta t$. The newly developed integrators thus provide further advantages for the MASH method, demonstrating that it can be implemented more efficiently than other surface-hopping approaches, which cannot construct time-reversible integrators due to their stochastic nature.